1. Technical Field
This invention relates to an area cutting method and, more particularly, to an area cutting method through which the interior of an area bounded by a closed curve can be cut efficiently.
2. Description of the Related Art
Forms of numerically controlled machining include cutting in which the interior of an area bounded by a closed curve is hollowed out down to a predetermined depth, and die milling in which the interior of an area is die milled. In such machining, as shown in FIG. 8(A), an area cutting method is conventionally carried out by performing cutting along an (i-1)th cutting path PTi=1 in one direction (the direction of the solid line arrow), raising the tool a predetermined amount at the completion of cutting, then positioning the tool directly above a cutting starting point Ps on the next, or i-th, cutting path PTi, thereafter lowering the tool to the cutting starting point Ps, moving the tool along the i-th cutting path PTi in the direction of the solid line arrow, and subsequently repeating the above unidirectional cutting.
Another area cutting method shown in FIG. 8(B) includes, following completion of cutting along the cutting path PTi-1 of the (i-1)th cutting path, moving the tool from a cutting end point Pe to the cutting starting point Ps on the next, or i-th, cutting path, and thereafter performing cutting along the i-th cutting path PTi. Thus, cutting is performed back and forth in the direction of the arrows.
Still another area cutting method shown in FIG. 8(C) includes obtaining offset paths OFC1, OFC2, . . . OFCn offset by predetermined amounts with respect to a curve OLC of an external shape, and moving the tool successively along the offset paths.
However, with the first area cutting method based on unidirectional cutting, the tool must be positioned at the cutting starting point Ps on the i-th cutting path PTi after the completion of cutting along the (i-1)th cutting path PTi-1. This method is disadvantageous in that it results in a long tool traveling distance.
With the second cutting method based on reciprocative cutting, portions are left uncut. In order to cut the uncut portions, the tool must be moved along the external shape curve OLC at completion of the back-and-forth cutting, thereby necessitating both back-and-forth cutting control and cutting control along the shape of the external curve. Accordingly, this method is disadvantageous in that control is complicated. Further, if an area AR has concavities and convexities, as shown in FIG. 8(D), the second method requires movement for achieving positioning indicated by the dashed lines. This is disadvantageous in that tool travelling distance and cutting time are prolonged. In addition, since the cutting process for the outward trip is different from the cutting process for the return trip, cutting cannot be performed efficiently overall. It should be noted that the cutting processes referred to here indicate up cutting and down cutting processes. FIGS. 9(A) and 9(B) show examples of the down cutting process, and FIGS. 9(C)/(D) depict examples of the up cutting process. If the workpiece material has been decided, then a cutting method capable of cutting the workpiece efficiently is selected from the up cutting and down cutting processes. However, with the second method, the up cutting process [e.g. FIG. 9(A)] and the down cutting process [e.g. FIG. 9(C)] are always mixed, so that cutting cannot be performed efficiently.
With the third method of cutting along the offset paths, portions are left uncut at, e.g., the central portion of the area, depending upon the contour of the external shape curve. This method is disadvantageous in that dealing with these uncut portions is a complicated task.
Accordingly, in order to eliminate the aforementioned drawbacks of the conventional method, the applicant has proposed a method in which a tool path in the form of a spider web pattern is decided within the area and a tool is moved along the tool path to machine the area. (For example, refer to the specification of U.S. Ser. No. 744,746.) FIGS. 10(A) and 10(B) are views for describing this area cutting method. The area cutting method is composed of the following steps:
(1) For cutting the interior of an area AR bounded by an external shape curve OLC comprising a number of straight lines S1, S2, . . . S6 and a circular arc A1, linearly approximating a circular arc portion A1' of an offset curve OFC offset a predetermined amount from the external shape curve;
(2) dividing an area bounded by the linearly approximated offset curve into a plurality of convex polygons PG1-PG3;
(3) calculating the centroid Wi of each convex polygon and the mid-points M1, M2 of boundary lines B1, B2 of two mutually adjacent convex polygons and generating a base line BL obtained by successively connecting each centroid and each mid-point;
(4) partitioning, into a predetermined number of partitions, straight lines L1-L14 connecting the centroids Wi of the convex polygons and the apices P1-P10 of the convex polygons, and straight lines BL1-BL4 connecting the mid-points M1, M2 and the two ends P1, P4; P4, P7 of the boundary lines bisected by the mid-points;
(5) moving a tool along plural closed paths CPT1, CPT2, . . . obtained by connecting partitioning points Pa1, Pa2, . . . Pa18; Pb1, Pb2, . . . Pb18, which correspond to the straight lines L1-L14, BL1-BL4, in such a manner that the base line BL is enclosed, and moving the tool along the base line BL, and
(6) moving the tool along the offset curve OFC.
According to this method, area cutting can be carried out while moving the tool continuously. This is advantageous in that it eliminates wasted tool movement and shortens cutting time in comparison with the prior-art method. It also does not leave any uncut portions at, e.g., the central part of the area.
However, if the sizes of the convex polygons differ greatly from one another in the proposed area cutting method, the cut-in pitch of a smaller convex polygon is considerably shorter than that of a larger convex polygon [(see the cut-in pitches t.sub.1, t.sub.2 of convex polygons PG1, PG2 in FIG. 10(B)].
It should be possible to cut the small convex polygonal portion at the cut-in pitch t.sub.2 of the large convex polygonal portion. If the small convex polygonal portion is cut at the larger cut-in pitch, cutting efficiency can improved.
With the conventional proposed method, however, the cut-in pitch of each convex polygonal portion is decided depending upon the size of the convex polygon. Consequently, the small convex polygonal portion is cut in at the small cut-in pitch, as a result of which cutting efficiency declines.